Leela invests $500 at 4.5% interest according to the equation , where Vl is the value of the account after t years. Adele invests the same amount of money at the same interest rate, but begins investing two years earlier according to the equation . The total value of Adele’s account is approximately what percent of the total value of Leela’s account at any time, t?
+2353 The value of leela's account can be calculated in the following way;
$$\begin{array}{lcl}
\mbox{At the beginning (year 0) }VI = 500\\
\mbox{After 1 year }VI = 500 \times 1.045\\
\mbox{After 2 years } VI = 500 \times 1.045 \times 1.045= 500 \times 1.045^2\\
\mbox{After t years } VI=500 \times 1.045^t\\
\mbox{Adele started 2 years earlier so by the time Leela started saving she already had }500*1.045^2 \mbox{ in her account}\\
\mbox{Therefore at year t Adele has }500*1.045^2*1.045^t = 500*1.045^{t+2} \mbox{ in her account}\\
\mbox{Therefore the percentage of value of Adele's account compared to Leela's account can be given by}\\
\frac{500*1.045^{t+2}}{500*1.045^t} \times 100\%= 1.045^2 \times 100\% = 1.092025 \times 100\% = 109.2025 \% \approx 109.20 \%
\end{array}$$
Reinout 
+2353 The value of leela's account can be calculated in the following way;
$$\begin{array}{lcl}
\mbox{At the beginning (year 0) }VI = 500\\
\mbox{After 1 year }VI = 500 \times 1.045\\
\mbox{After 2 years } VI = 500 \times 1.045 \times 1.045= 500 \times 1.045^2\\
\mbox{After t years } VI=500 \times 1.045^t\\
\mbox{Adele started 2 years earlier so by the time Leela started saving she already had }500*1.045^2 \mbox{ in her account}\\
\mbox{Therefore at year t Adele has }500*1.045^2*1.045^t = 500*1.045^{t+2} \mbox{ in her account}\\
\mbox{Therefore the percentage of value of Adele's account compared to Leela's account can be given by}\\
\frac{500*1.045^{t+2}}{500*1.045^t} \times 100\%= 1.045^2 \times 100\% = 1.092025 \times 100\% = 109.2025 \% \approx 109.20 \%
\end{array}$$
Reinout
